Bayesian multilevel multidimensional item response modeling approach for multiple latent variables in a hierarchical structure

In this paper, we propose a multilevel multidimensional item response model for studying the relations among multiple abilities and covariates in a hierarchical data structure. As an example, this study is well suited to examining the scenario in which a test measures multidimensional latent traits (e.g., reading ability, cognitive ability, and computing ability) and in which students are nested within classes or schools. The new model can recover the correlations among multidimensional abilities, along with the correlation between person- and school-level covariates and abilities. A fully Gibbs sampling algorithm within the Markov chain Monte Carlo (MCMC) framework is proposed for parameter estimation. A unique form of the deviance information criterion (DIC) is used as a model comparison index. Two simulation studies show that the estimation method is suitable in recovering all model parameters.